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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Reduced Power reflection principles Cardinal Invariants Cardinal function Hedetniemi's conjecture Fodor-type reflection Large Cardinals polarized partition relation Ostaszewski square Microscopic Approach Hindman's Theorem Sakurai's Bell inequality weak diamond projective Boolean algebra square 20M14 HOD Universal Sequences coloring number Mandelbrot set OCA Distributive tree Almost countably chromatic approachability ideal Singular coﬁnality Aronszajn tree Coherent tree stationary reflection Dushnik-Miller Partition Relations Slim tree tensor product graph Ascent Path very good scale Postprocessing function Erdos-Hajnal graphs Knaster Prikry-type forcing Absoluteness Uniformization Kurepa Hypothesis Foundations Rainbow sets Singular cardinals combinatorics Antichain Singular Density Parameterized proxy principle Uniformly coherent Generalized Clubs Minimal Walks P-Ideal Dichotomy S-Space Cohen real Selective Ultrafilter 05A17 Chromatic number Poset Erdos Cardinal Commutative cancellative semigroups xbox sap middle diamond Weakly compact cardinal L-space ccc Souslin Tree Shelah's Strong Hypothesis b-scale Non-saturation weak square stationary hitting Martin's Axiom Stevo Todorcevic Chang's conjecture Forcing Axioms Jonsson cardinal Almost-disjoint famiy Club Guessing square principles Successor of Regular Cardinal Fat stationary set 11P99 PFA(S)[S] Rock n' Roll Hereditarily Lindelöf space Small forcing Diamond Whitehead Problem Almost Souslin Prevalent singular cardinals free Boolean algebra Fast club Constructible Universe Axiom R Rado's conjecture Square-Brackets Partition Relations diamond star Successor of Singular Cardinal PFA 05D10 Forcing incompactness Nonspecial tree

# Tag Archives: 03E50

## Jensen’s diamond principle and its relatives

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading